Vortex Methods for Direct Numerical Simulation of Three-Dimensional Bluff Body Flows: Application to the Sphere at Re=300, 500, and 1000

Recent contributions to the 3-D vortex methods are presented. Following Cottet, the particles strength exchange (PSE) scheme for diffusion is modified in the vicinity of solid boundaries to avoid a spurious vorticity flux and to enforce a zero-normal component of vorticity during the convection/PSE step. The vortex sheet algorithm used to enforce the no-slip boundary condition through a vorticity flux at the boundary and the technique used to perform accurate redistributions in the presence of bodies of general geometry are extended from their 2-D counterpart. To perform simulations with nonuniform resolution, a mapping of the redistribution lattice is used. Computational efficiency is attained through the use of parallel tree codes based on multipole expansions of vortex particles and of vortex panels. The method is validated, by comparisons with other authors' results, on the flow past a sphere at Re=300. It is then applied to compute the flow at Re=500 and 1000.